{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Updating with Conjugate Priors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When the data consists of binary Bernoulli random variables with a certain success probability for a positive outcome, the number of successes in repeated trials follows a Binomial distribution. The conjugate prior is the Beta distribution with support over the interval [0, 1] and two shape parameters to model arbitrary prior distributions over the success probability. Hence, the posterior distribution is also a Beta distribution that we can derive by directly updating the parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T23:44:42.815620Z",
     "start_time": "2020-06-17T23:44:42.806259Z"
    }
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T23:44:43.350186Z",
     "start_time": "2020-06-17T23:44:42.817444Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "import scipy.stats as stats\n",
    "from matplotlib.ticker import FuncFormatter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T23:44:43.353769Z",
     "start_time": "2020-06-17T23:44:43.351163Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "mpl.rcParams['text.usetex'] = True\n",
    "mpl.rcParams['text.latex.preamble'] = [r'\\usepackage{amsmath}']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T23:44:43.367473Z",
     "start_time": "2020-06-17T23:44:43.356066Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "sns.set_style('dark')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formatting Helper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T23:44:43.376432Z",
     "start_time": "2020-06-17T23:44:43.368323Z"
    }
   },
   "outputs": [],
   "source": [
    "def format_plot(axes, i, p, y, trials, success, true_p, tmle, tmap=None):\n",
    "    fmt = FuncFormatter(lambda x, _: f'{x:.0%}')\n",
    "    if i >= 6:\n",
    "        axes[i].set_xlabel(\"$p$, Success Probability\")\n",
    "        axes[i].xaxis.set_major_formatter(fmt)\n",
    "    else:\n",
    "        axes[i].axes.get_xaxis().set_visible(False)\n",
    "    if i % 3 == 0:\n",
    "        axes[i].set_ylabel(\"Posterior Probability\")\n",
    "    axes[i].set_yticks([], [])\n",
    "\n",
    "    axes[i].plot(p, y, lw=1, c='k')\n",
    "    axes[i].fill_between(p, y, color='darkblue', alpha=0.4)\n",
    "    axes[i].vlines(true_p, 0, max(10, np.max(y)), color='k', linestyle='--', lw=1)\n",
    "    axes[i].set_title(f'Trials: {trials:,d} - Success: {success:,d}')\n",
    "    if i > 0:\n",
    "        smle = r\"$\\theta_{{\\mathrm{{MLE}}}}$ = {:.2%}\".format(tmle)\n",
    "        axes[i].text(x=.02, y=.85, s=smle, transform=axes[i].transAxes)\n",
    "        smap = r\"$\\theta_{{\\mathrm{{MAP}}}}$ = {:.2%}\".format(tmap)\n",
    "        axes[i].text(x=.02, y=.75, s=smap, transform=axes[i].transAxes)    \n",
    "    return axes[i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate Coin Tosses & Updates of Posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T23:44:48.608283Z",
     "start_time": "2020-06-17T23:44:43.377925Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x504 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_trials = [0, 1, 3, 5, 10, 25, 50, 100, 500]\n",
    "outcomes = stats.bernoulli.rvs(p=0.5, size=n_trials[-1])\n",
    "p = np.linspace(0, 1, 100)\n",
    "# uniform (uninformative) prior\n",
    "a = b = 1\n",
    "\n",
    "fig, axes = plt.subplots(nrows=3, ncols=3, figsize=(14, 7), sharex=True)\n",
    "axes = axes.flatten()\n",
    "fmt = FuncFormatter(lambda x, _: f'{x:.0%}')\n",
    "for i, trials in enumerate(n_trials):\n",
    "    successes = outcomes[:trials]\n",
    "    theta_mle = np.mean(successes)\n",
    "    heads = sum(successes)\n",
    "    tails = trials - heads\n",
    "    update = stats.beta.pdf(p, a + heads , b + tails)\n",
    "    theta_map = pd.Series(update, index=p).idxmax()\n",
    "    axes[i] = format_plot(axes, i, p, update, trials=trials, success=heads, \n",
    "                          true_p=.5, tmle=theta_mle, tmap=theta_map)\n",
    "\n",
    "title = 'Bayesian Probabilities: Updating the Posterior'\n",
    "fig.suptitle(title,  y=1.02, fontsize=14)\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stock Price Moves"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will collect samples of different sizes of binarized daily S&P 500 returns where the positive outcome is a price increase. Starting from an uninformative prior that allocates equal probability to each possible success probability in the interval [0, 1], we compute the posterior for different evidence samples. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T23:44:55.541585Z",
     "start_time": "2020-06-17T23:44:55.525278Z"
    }
   },
   "outputs": [],
   "source": [
    "sp500_returns = pd.read_hdf('../data/assets.h5', key='sp500/fred').loc['2010':, 'close']\n",
    "sp500_binary = (sp500_returns.pct_change().dropna() > 0).astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code sample shows that the update consists in simply adding the observed numbers of success and failure to the parameters of the prior distribution to obtain the posterior.\n",
    "\n",
    "The resulting posterior distributions are plotted below. They illustrate the evolution from a  uniform prior that views all success probabilities as equally likely to an increasingly peaked distribution.\n",
    "After 500 samples, the probability is concentrated near the actual probability of a positive move at 54.7% from 2010 to 2017. It also shows the small differences between MLE and MAP estimates, where the latter tends to be pulled slightly towards the expected value of the uniform prior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T23:45:01.530892Z",
     "start_time": "2020-06-17T23:44:57.326134Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x504 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_days = [0, 1, 3, 5, 10, 25, 50, 100, 500]\n",
    "# random sample of trading days\n",
    "# outcomes = sp500_binary.sample(n_days[-1])\n",
    "\n",
    "# initial 500 trading days\n",
    "outcomes = sp500_binary.iloc[:n_days[-1]]\n",
    "p = np.linspace(0, 1, 100)\n",
    "\n",
    "# uniform (uninformative) prior\n",
    "a = b = 1\n",
    "\n",
    "fig, axes = plt.subplots(nrows=3, ncols=3, figsize=(14, 7), sharex=True)\n",
    "axes = axes.flatten()\n",
    "for i, days in enumerate(n_days):\n",
    "    successes = outcomes.iloc[:days]\n",
    "    theta_mle = successes.mean()\n",
    "    up = successes.sum()\n",
    "    down = days - up\n",
    "    update = stats.beta.pdf(p, a + up , b + down)\n",
    "    theta_map = pd.Series(update, index=p).idxmax()\n",
    "    axes[i] = format_plot(axes, i, p, update, trials=days, success=up, \n",
    "                          true_p=sp500_binary.mean(), tmle=theta_mle, tmap=theta_map)\n",
    "\n",
    "title = 'Bayesian Probabilities: Updating the Posterior'\n",
    "fig.suptitle(title,  y=1.02, fontsize=14)\n",
    "fig.tight_layout()"
   ]
  }
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